Breast Cancer Classification: A Statistical Evaluation of Dimensionality Reduction

Abstract

Breast cancer is one of the leading causes of cancer-related mortality among women worldwide. Although machine learning models have demonstrated high performance in breast tumor classification, the impact of dimensionality reduction on predictive performance remains insufficiently explored. This study evaluates the effect of linear and nonlinear dimensionality reduction techniques on breast cancer classification using the Breast Cancer Wisconsin Original dataset. Seven supervised learning algorithms were optimized through grid search and evaluated using stratified cross-validation, balanced accuracy, AUC-ROC, bootstrap confidence intervals, and statistical hypothesis testing. Feature relevance and redundancy were analyzed prior to dimensionality reduction using Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP). Support Vector Machines and Random Forest achieved the highest balanced accuracy, both reaching 0.9678 on the test set. Feature analysis revealed substantial redundancy among several cytological variables. PCA retained 96.1% of the total variance using seven components, reducing dimensionality by 22.2% without statistically significant performance degradation. In contrast, UMAP reduced the feature space to two or three dimensions but produced small yet significant reductions in balanced accuracy and AUC-ROC. These results indicate that the WBCO dataset contains considerable redundant information and that dimensionality reduction can simplify predictive models while preserving diagnostic performance. PCA provided the best trade-off between dimensionality reduction and classification accuracy.